Here's what you want to do.
Upgrade iPhoto 11 to the latest version.
Open the Library with it.
Then open the Library with the latest version of Aperture.
No importing as the latest versions of both apps can use the same Library.
I noted this:
We tried to update the library to iPhoto 11 on the new iMac, and that hangs.
Try rebuild the Library:
Back Up and try rebuild the library: hold down the command and option (or alt) keys while launching iPhoto. Use the resulting dialogue to rebuild. Choose to Repair Database. If that doesn't help, then try again, this time using Rebuild Database.
If that fails:
Download iPhoto Library Manager and use its rebuild function. (In Library Manager it's the FIle -> Rebuild command)
This will create an entirely new library. It will then copy (or try to) your photos and all the associated metadata and versions to this new Library, and arrange it as close as it can to what you had in the damaged Library. It does this based on information it finds in the iPhoto sharing mechanism - but that means that things not shared won't be there, so no slideshows, books or calendars, for instance - but it should get all your events, albums and keywords, faces and places back.
Because this process creates an entirely new library and leaves your old one untouched, it is non-destructive, and if you're not happy with the results you can simply return to your old one.